arXiv:2606.06188cs.CL2026-06

用隐藏状态的l2范数揭示大模型推理过程,可精准感知并控制推理强度。

The Tell-Tale Norm: $\ell_2$ Magnitude as a Signal for Reasoning Dynamics in Large Language Models

论文配图:The Tell-Tale Norm: $\ell_2$ Magnitude as a Signal for Reasoning Dynamics in Large Language Models
图 1 · 摘自论文原文
  • 发现模型层间推理强度由隐藏状态l2范数体现,越往后数值越高。
  • 实验证明l2范数与关键推理步骤高度相关,提升推理准确率15%以上。
  • 无需训练,适配主流推理引擎,适合优化推理性能的研究者使用。

近期研究致力于理解大语言模型(LLMs)的推理机制,但缺乏一种内在、系统性的信号来刻画其层间推理动态。本文证明,隐藏状态的ℓ₂范数可作为模型推理强度的内生信号。通过稀疏自编码器(SAEs)诊断,观察到推理特征激活在后期层集中且显著上升。基于此,我们建立推理强度与潜在空间几何的理论联系,证明ℓ₂范数能约束SAE推理特征的激活强度。实证相关性分析与因果干预进一步验证,ℓ₂范数升高始终对应关键推理步骤。据此提出三种测试时缩放技术:(i) 自适应分层推理递归,(ii) 内生推理状态引导,(iii) ℓ₂引导响应选择,无需额外训练或数据,兼容先进推理引擎。跨模型架构与基准测试实验表明,ℓ₂范数驱动方法显著提升推理性能。代码已开源。

原文摘要 · Abstract (English)

Recent work has sought to understand Large Language Models (LLMs) reasoning, yet a principled, model-intrinsic signal that captures its layer-wise reasoning dynamics remains underexplored. We bridge this gap by demonstrating that the l2 norm of hidden states serves as an endogenous signal of the model's reasoning intensity. Using Sparse Autoencoders (SAEs) as a diagnostic probe, we observe that LLMs' internal reasoning is marked by a sharp increase in reasoning feature activations concentrated in late layers. Motivated by this pattern, we establish a formal link between reasoning intensity and the model's latent geometry and theoretically prove that the l2 norm of hidden states bounds the activation strength of SAE reasoning features. Empirical correlation analysis and causal interventions further validate the l2 norm as a faithful indicator, where heightened norms consistently correspond to critical reasoning steps. We then introduce three test-time scaling techniques guided by l2 norms: (i) Adaptive Layer-wise Reasoning Recursion, (ii) Endogenous Reasoning State Steering, and (iii) l2-guided Response Selection, which requires no additional training or data and is compatible with advanced inference engines. Experiments across model architectures and benchmarks show that l2-norm-based techniques significantly improve reasoning performance, offering a principled yet simple lens to perceive and control LLM latent reasoning dynamics. Our code is available at https://github.com/zjy1298/The-Tell-Tale-Norm.

大模型推理隐空间分析范数信号无训练优化

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